The 30-year-old model has been spotted with the Hollywood star a lot in recent weeks and their romance is progressing well.
"They've been spending more and more time together. He hasn't been brought around the family yet," a source told People.
Despite this, Jenner's family is supportive of her new romance.
The Jenner-Kardashian family haven't yet met Elordi, but they can see the positive impact he's already had on the brunette beauty, who has previously dated the likes of Bad Bunny, Devin Booker and Ben Simmons.
"The family is hearing Kendall is happy, but the family doesn't know him well yet," the insider shared.
A source recently claimed that Jenner and Elordi are "figuring things out naturally".
The celebrity duo were seen on a tropical getaway in Hawaii in recent weeks, but they're determined to take things slowly while they decide where they stand with each other.
"They're not trying to turn this into some big public thing. They enjoy spending time together in more private settings," an insider told People.
Jenner has grown fond of Elordi very quickly, but they don't want to move too fast.
"They want to keep things low-key while they're figuring things out naturally," the source said.
"Kendall really likes him, though."
Meanwhile, Jenner previously admitted to feeling frustrated by the rumours surrounding her sexuality.
"There's the whole side of the internet that thinks I'm a lesbian," she said on the In Your Dreams podcast.
"You want to know what really bothers me? How mean people are about it. It's not with, like, a welcoming arm of like, 'Hey, if you were, yes, come join.' It's not kind. It's very mean. It's very like, 'What the f**k are you doing?'"
She says she wouldn't have any issues being public about her sexuality if she was gay.
"I understand that coming out is not an easy thing for anybody, if not most people. And I'm not saying that's an easy thing, but knowing, and I can speak for myself here, and knowing myself, I think at this point in my life I'd be out if I was," she said.
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